Method for aquiring and processing marine seismic data to extract and constructively use the up-going and down-going wave-fields emitted by the source(s)

ABSTRACT

A method for acquisition and processing of marine seismic signals to extract up-going and down- going wave-fields from a seismic energy source includes deploying at least two marine seismic energy sources at different depths in a body of water. These seismic energy sources are actuated with known time delays that are varied from shot record to shot record. Seismic signals from sources deployed at different depths are recorded simultaneously. Seismic energy corresponding to each of the sources is extracted from the recorded seismic signals. Up-going and down-going wave-fields are extracted from the sources deployed at different depths using the extracted seismic energy therefrom. A method includes the separated up-going and down-going wave-fields are propagated to a water surface or a common reference, the up-going or the down-going wave-field is 180 degree phase shifted, and the signals from these modified up-going and down-going wave-fields are summed.

CROSS-REFERENCE TO RELATED APPLICATIONS

Not applicable.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to the fields of marine seismic dataacquisition and data processing. More particularly the invention relatesto methods for designing and actuating marine seismic sources, and forprocessing such data, in which the up-going and down-going wave-fieldemitted by the source can be extracted and added constructively.

2. Background Art

In seismic exploration, seismic data are acquired by imparting acousticenergy into the Earth near its surface, and detecting acoustic energythat is reflected from boundaries between different layers of subsurfacerock formations. Acoustic energy is reflected when there is a differencein acoustic impedance between adjacent layers to a boundary. Signalsrepresenting the detected acoustic energy are interpreted to inferstructures and composition of the subsurface rock formation structures.

In marine seismic exploration, a seismic energy source, such as an airgun, or air gun array, is typically used to impart the acoustic energyinto the formations below the bottom of the water. The air gun or arrayis actuated at a selected depth in the water, typically while the airgun or array is towed by a vessel. The same or a different vessel towsone or more seismic sensor cables, called “streamers”, in the water.Generally the streamer extends behind the vessel along the direction inwhich the streamer is towed. Typically, a streamer includes a pluralityof hydrophones disposed on the cable at spaced apart, known positionsalong the cable. Hydrophones, as is known in the art, are sensors thatgenerate an optical or electrical signal corresponding to the pressureof the water or the time gradient (dp/dt) of pressure in the water. Thevessel that tows the one or more streamers typically includes recordingequipment to make a record, indexed with respect to time, of the signalsgenerated by the hydrophones in response to the detected acousticenergy. The record of signals is processed, as previously explained, toinfer structures of and compositions of the earth formations below thelocations at which the seismic survey is performed.

Marine seismic data include an effect that limits the accuracy ofinferring the structure and composition of the subsurface rockformations. This effect, known as source ghosting, arises because waterhas a substantially different density and propagation velocity ofpressure waves than the air above the water surface. Source ghosting canbe understood as follows. When the air gun or air gun array is actuated,acoustic energy radiates generally outwardly from the air gun or array.Half of the energy travels downwardly where it passes through the waterbottom and into the subsurface rock formations. The other half of theacoustic energy travels upwardly from the gun or array and most of thisenergy reflects from the water surface whereupon it travels downwardly.The reflected acoustic energy will be delayed in time and also beshifted in phase by about 180 degrees from the directly downwardpropagating acoustic energy. The surface-reflected, downwardly travelingacoustic energy is commonly known as a “ghost” signal. The ghost signalinterferes with the directly downward propagating wave-field causingconstructive interference in some parts of the frequency band anddestructive interference in other parts of the frequency band. Thiscauses a sequence of notches in the spectrum, equally spaced infrequency including a notch at zero frequency (0 Hz). The frequencies ofthese notches in the detected acoustic signal are related to the depthat which the air gun or gun array is disposed, as is well known in theart. The effect of the source ghosting is typically referred to as the“source ghost.”

The seismic energy emitted by the source is attenuated with propagationdistance because of geometrical spreading, transmission loss, andabsorption. The absorption of higher-frequency energy at a greater ratethan lower-frequency energy is well known in the art. Therefore, fordeep penetration it is a desire to maximize the energy emitted by thesource at lower frequencies. Since the source ghost has a notch at 0 Hz,it is limiting the energy in the low-frequency end. This may be improvedby towing the sources at a greater depth. However, this causes the ghostnotches in the spectrum to occur at lower frequencies, and hence limitsthe high frequency parts of the spectrum needed for high resolutionimaging of shallower targets. Also, when using air gun(s) as a seismicenergy source, the fundamental frequency of the gun(s) increases withincreasing depth. Hence, the increase in energy in the low frequency endwhen towing the air-guns deeper due to the source ghost, is counteractedby the increase in fundamental frequency of the air-gun(s).

A traditional way of increasing the signal level emitted by the sourceacross the bandwidth when using air-gun(s) is to increase the totalvolume of air released by the air-gun(s) and/or to increase theoperating pressure. However, the maximum volume of air that can bereleased for every shot and the maximum air pressure is limited by theavailable source equipment and air-supply system. To change this can bevery expensive and time consuming. Also, increasing the source strengthmay have an impact on marine life. Therefore, maximizing the use of thesignal emitted by the source may be of great value and reduce the needto increase the energy level emitted by the source. By extracting theupward (ghosted) and the directly downward propagating wave-fields fromthe source, the effects of the source ghost are eliminated and thesignal around all ghost notches is boosted including the notch at 0 Hz.These separated wave-fields can also be time shifted to the sea-surfaceor a common reference depth using the known source depth(s), then byapplying a 180 phase shift to the ghosted signal, they can be summedtogether constructively. In this way almost all energy emitted by thesource is utilized, which consequentially almost doubles the primaryenergy level for a given energy source.

A technique known in the art for extracting the source ghost isdescribed in M. Egan et al., Full deghosting of OBC data with over/undersource acquisition, 2007 Annual Meeting, San Antonio, Tex., Society ofExploration Geophysicists. The technique described in the Egan et al.publication includes towing a first seismic energy source at a firstdepth in the water, and towing a second seismic energy source at asecond depth in the water. The sources are air guns or arrays thereof.The second source is also towed at a selected distance behind the firstsource. The first source is actuated and seismic signals are recordedcorresponding to actuations of the first source. After the towing vesselhas moved so that the second source is disposed at substantially thesame geodetic position as the first source was at the time of itsactuation, the second source is actuated and seismic signals are againrecorded. A “deghosted” seismic data set is obtained using the techniquedescribed more fully in the Egan et al. publication.

One of the main issues with the over/under source technique described inthe Egan et al. publication referred to above is that the number of shotpositions is half compared to conventional source actuation techniquescausing the fold coverage to be half. Another issue with this technique,if the seismic receivers are towed behind a vessel and hence moving fromshot to shot, is that the receivers have moved a considerable distancebetween when the sources at different depths are actuated. To maintainthe number of shot positions and fold coverage as in conventional marineseismic acquisition, and to minimize the difference in receiverpositions when the sources at different depths are actuated, it isdesirable to have a method for extracting the source ghost that allowssources towed at different depths to be actuated during the recording ofeach shot record.

A technique known in the art for actuating multiple sources during therecording of each shot record is described in U.S. Pat. No. 6,882,938issued to S. Vaage and commonly owned with the present invention. In thedescribed technique, multiple sources are actuated with selectedvariable time delays relative to the start of the seismic recording. Thewave-fields emitted by each individual source can be extracted by usingthe coherency of the signals from one source in certain domains aftercorrecting for the known time delays of actuating that source.

SUMMARY OF THE INVENTION

A method according to one aspect of the invention for acquisition andprocessing of marine seismic signals to extract up-going and down-goingwave-fields from a seismic energy source includes deploying at least twomarine seismic energy sources at different depths in a body of water andat substantially a same longitudinal position with respect to a seismicvessel. These seismic energy sources are actuated with known time delaysthat are varied from shot record to shot record. Seismic signals fromeach of the sources are recorded simultaneously. Seismic energycorresponding to each of the source is extracted from the recordedseismic signals. Up-going and down-going wave-fields are extracted foreach of the sources using the extracted seismic energy therefrom.

A method for marine seismic surveying according to another aspect of theinvention uses separated up-going and down-going wave-fields from aseismic energy source. The separated up-going and down-going wave-fieldsare propagated to at least one of a water surface and a common referencedepth. One of the up-going or down-going wave-field is shifted 180degrees in phase. Finally these modified up-going and down-goingwave-fields are summed.

A method according to another aspect of the invention for marine seismicsurveying using at least two seismic energy sources operated atdifferent depths and at substantially a same source geodetic positionincludes separating energy from each of the sources from the recordedsignals. Up-going and down-going wave-fields corresponding to eachsource are extracted from the separated energy. The extracted up-goingand down-going wave-fields from each source are propagated to at leastone of a water surface and a common reference depth. One of thepropagated wave-fields is shifted 180 degrees in phase. The phaseshifted, propagated wave-fields are summed.

Other aspects and advantages of the invention will be apparent from thefollowing description and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows acquiring seismic data in cross section to show an examplearrangement of seismic energy sources.

FIG. 2 shows a plan view of acquiring seismic data to show an examplearrangement of seismic receiver streamers.

FIG. 3 shows a flow chart of example processes according to theinvention.

FIG. 4 shows an example of spectral output of a single seismic sourcewith that of combined seismic sources operated according to theinvention.

DETAILED DESCRIPTION

FIG. 1 shows in cross sectional view an example arrangement foracquiring seismic data according to the invention. A seismic surveyvessel 10 moves along the surface 11A of a body of water 11 such as alake or the ocean. The vessel 10 typically includes equipment showngenerally at 12 and referred to for convenience as a “recording system.”The recording system 12 may include devices (none shown separately) forselectively actuating seismic energy sources 14, 16 (explained below),for actuating and recording the signals generated by the sensors orreceivers 20 (explained below) in response to seismic energy impartedinto the water 11 and thereby into rock formations 19, 21 below thewater bottom 13, and for determining geodetic position of the vessel 10,the seismic energy sources 14, 16 and each of a plurality of seismicsensors or receivers 20 at any time.

The vessel 10 is shown towing two seismic energy sources 14, 16. Theseismic energy sources 14, 16 can be any type of marine energy sourceincluding but not limited to air guns and water guns, or arrays of suchenergy sources. In the example shown in FIG. 1, the sources 14, 16 aretowed at substantially the same distance behind the vessel 10 and atdifferent depths in the water 11. In other examples, the sources 14, 16may be towed by a different vessel (not shown), or may be in a fixedposition (provided that the depths are different as shown in FIG. 1).Therefore, having the survey vessel 10 tow the sources 14, 16 is not alimit on the scope of the present invention.

The vessel 10 is also shown towing a seismic streamer 18. However, thisinvention is generally related to the energy source, and therefore maybe used together with any type of towed seismic streamer in anyconfiguration, ocean bottom cable, sensors deployed in boreholes etc.,and with any type of receiving sensor including but not limited topressure sensors, pressure time gradient sensors, velocity sensors,accelerometers etc., or any combination thereof.

During operation of the arrangement in FIG. 1, at selected times after afirst delay time relative to start of the seismic recording theacquisition system 12 actuates a first one of the seismic energysources, e.g., source 14. Energy from the first source 14 travelsoutwardly therefrom as shown at 24. Some of the energy travelsdownwardly where it is reflected at acoustic impedance boundaries, e.g.,the water bottom 13 and at the boundaries 15, 17 between different rockformations 19, 21. Only the water bottom reflections are shown in FIG. 1for clarity of the illustration. Up-going portions of the energy fromthe first source 14 are reflected from the water surface 11A as shown inFIG. 1. The recording system 12 is configured to actuate the secondseismic energy source, e.g., source 16, at the end of a second selectedtime delay relative to the start of the seismic data recording, or,alternatively, after a selected time before or after the actuation ofthe first source 14. Energy travelling outwardly from the second source16 moves along similar paths as the energy from the first source 14 asshown at 22 in FIG. 1. In the present invention, each actuation of boththe first and second seismic energy sources with the above describedtime delays may be referred to as a “firing sequence.” The time delaysvary from firing sequence to firing sequence in a known, random,semi-random or systematic manner. Typically, the time delays are lessthan one second, but may also be longer. It is also important for thetime delays for the firing of the sources to be different in each firingsequence. The difference in time delay between firing the first sourceand the second source should also vary in a known manner which may berandom, semi-random or systematic.

FIG. 2 shows the arrangement of FIG. 1 in plan view to illustrate towinga plurality of laterally spaced apart streamers 18. The streamers 18 canbe maintained in their relative lateral and longitudinal positions withrespect to the vessel 10 using towing equipment 23 of types well knownin the art. What is also shown in FIG. 2 is that the first source 14 andthe second source 16 can be laterally displaced (and/or longitudinallydisplaced in other examples) to avoid, in the case the sources 14, 16are air guns or arrays thereof, having dispersed air in the water 11from first source 14 affect the upwardly traveling seismic energy fromthe second source 16. Lateral and/or longitudinal displacement iscontemplated as being only a few meters so that the sources 14, 16provide energy equivalent to being that which would occur if the sources14, 16 were in the same vertical plane and at the same longitudinaldistance behind the vessel, or expressed differently, at essentially thesame geodetic position. By avoiding having dispersed air above thesecond source 16 when actuated, the effects of the water surface (11A inFIG. 1) will be, adjusted for water depth, substantially the same as theeffect thereof on the first source (14 in FIG. 1).

The source actuation and signal recording explained above is repeatedfor a plurality of firing sequences while the vessel 10, sources 14, 16and streamers 18 move through the water 11. The signal recordings madefor each firing sequence by the recording system 12 may be referred toas a “shot record”, and each such shot record will include, for eachreceiver 20, signals corresponding to the seismic energy produced byboth the first source 14 and the second source 16.

An example method according to the invention will now be explained withreference to the flow chart in FIG. 3. At 100 the first source (14 inFIG. 1) is actuated.

Such actuation may be performed using a time delay with respect to thestart of seismic signal recording.

At 102, the second source (16 in FIG. 1) may be actuated in a pluralityof firing sequences with a different time delay. The time delay betweenthe actuation of the first source and the second source needs to varyfrom firing sequence to firing sequence, and may be negative such thatthe actuation of the second source may precede the actuation of thefirst source. The above firing of the first and second sources usingvariable time delays with respect to recording time may be repeated fora plurality of firing sequences. For each such firing sequence, thereceivers in each streamer measure a signal, as shown at 104 and also asexplained above. The recording system (12 in FIG. 1) may make recordingsof the signals produced by the receivers in each firing sequence, againas explained above.

At 106, the measured signals may be sorted into common receiver positiongathers or some other gather consisting of traces from different shotrecords. A common receiver position gather is a set of traces selectedfrom the shot records in which for each trace the receiver is located atsubstantially the same geodetic position at the time of recording of therespective traces. Referring back to FIG. 1, a first firing sequence maygenerate a signal (“trace”) for the receiver 20 nearest the vessel 10,for example. When the vessel 10 has moved so that the next receiver 20along the streamer 18 is located at substantially the same geodeticposition as was the nearest receiver at the time of the first firingsequence, the sources 14, 16 may be actuated as explained above in asecond firing sequence. The traces recorded from the second receiver 20in the second firing sequence will represent a common receiver positionrecord with respect to the traces recorded from the first receiver inthe first firing sequence. Because the geodetic positions of thereceivers 20 may be determined by the equipment (not shown separately)in the recording system 12 in each firing sequence, sorting theprocessed traces into common receiver position gathers may includeselecting traces in which the geodetic positions of the receiver fromwhich the traces are generated are substantially the same.

Referring once again to FIG. 3, at 108, the received signals may be timealigned to the actuation time of the first source. In some examples, theactuation time of the first source and the start of recording time maybe identical and such time alignment may not be used in such examples.Time alignment may be performed, for example, by time shifting eachtrace in each common receiver position gather by the time delay of thefirst source in each firing sequence with respect to the start of thesignal recording time. The energy from the first source that has beentime aligned will then be coherent in the receiver gather, whereas theenergy for the second source will be incoherent. At 110, a coherencyfilter or other technique may be applied to the common receiver positiontrace gathers after time alignment with respect to firing the firstsource if required to extract the portion of the recorded signalsresulting from the first source (14 in FIG. 1). Techniques forextracting signals from individual sources actuated into the sameseismic records with variable time delays are described, for example inP. Akerberg, et al., Simultaneous source separation by sparse radontransform, 2008 Annual Meeting, Las Vegas, Nev., Society of ExplorationGeophysicists. Another technique is described in, S. Spitz, Simultaneoussource separation: a prediction-subtraction approach, 2008 AnnualMeeting, Las Vegas, Nev., Society of Exploration Geophysicists.

At 112, the common receiver position gathers may then be time-aligned tothe actuation time of the second source (16 in FIG. 1) in each firingsequence. Time alignment may be performed, for example, by time shiftingeach trace in each common receiver position gather by the time delay ineach firing sequence. At 114, coherency filtering, or, for example, thetechnique described in the Akerberg et al. publication, substantially asexplained above with reference to 110 in FIG. 3 may be performed on thesecond source time aligned common shot record traces.

At 116, the up-going and down-going component signals resulting from thefirst source and from the second source may be used in a so-called“over/under” processing technique to extract the effect of the sourceghost. One example of such a technique is described in, M. Egan et al.,Full deghosting of OBC data with over/under source acquisition, 2007Annual Meeting, San Antonio, Tex., Society of Exploration Geophysicists,referenced in the Background section herein. The technique described inthe Egan et al. reference is based on a dual streamer techniquedescribed in, B. Posthumus, Deghosting using a twin streamerconfiguration, 52^(nd) annual meeting, Copenhagen, Denmark, EuropeanAssociation of Geoscientists and Engineers, 1990. To summarize themethod described in the Posthumus publication as applied to the presentinvention, seismic signals originating from the first source are phaseand amplitude corrected with respect to seismic signals originating fromthe second source, and the corrected signals are added as a weighted sumto generate deghosted signals. Techniques for separating up-going anddown-going wave-fields with an over/under configuration is described inD. Monk, Wavefield separation of twin streamer data, First Break Vol. 8,No. 3, March 1990.

Previous work on the over/under method has focused on application toseismic receivers operated at different depths in a body of water (seethe references cited above). The seismic receivers typically haveidentical responses (amplitude and phase) at all applicable depths.Therefore there is no need to apply response corrections beforecombining the data sets from the two (or more) depths. The same is nottrue when the methodology is applied to seismic energy sources, becausethe wave-field of marine seismic energy sources is substantiallysensitive to the hydrostatic pressure, which in turn is a function ofsource depth. Therefore, in the over/under methodology as applied toseismic energy sources there is an additional correction for the sourceresponses that needs to be applied. Note that such correction would beunnecessary if the individual source responses were specificallydesigned to be close to identical at a selected reference depth with thesources themselves operating at different depths. There are a variety ofknown techniques for designing, measuring or calculating the wave-fieldsof seismic sources, which have different levels of accuracy. Thewave-field or selected positions in the wave-field can be measureddirectly (e.g. far-field measurement) or the wave-field can becalculated based on physical models of the source. There are alsovarious methods of source monitoring, which determine the wave-field ofthe source array from shot to shot, using various sensors disposed onthe seismic source array. These include the so-called Notional sourcemethod, by Anton Ziolkowski et al. (1982) and, for example, Method ofSeismic Source Monitoring Using Modeled Source Signatures withCalibration Function, U.S. Pat. No. 7,218,572 issued to Parkes andcommonly owned with the present invention.

A result of the over/under wave-field separation is, at 116, thedirectly downward propagating energy and the up-going ghosted energyfrom both sources separated into separate wave-fields.

These separated up-going and down-going wave-fields are, at 118,propagated to the sea-surface or to any selected common reference depthbased on known towing depths of the sources. The propagation may beperformed using angle dependent time shifting based on known sourcedepths and angle of the received incoming wave-fronts, or by linearphase shifting if the propagation is performed in the frequency domain.Since the sea-surface (water surface) represents a negative reflectioncoefficient, the up-going (ghosted) wave-field is then 180 degree phaseshifted at 120. Finally the up-going and down-going wave-fields may besummed at 122. In this way, most of the energy emitted by the twosources can be used constructively.

FIG. 4 shows a graph of the energy output with respect to frequency of aair-gun source array, at curve 80 contrasted with a graph at 82 ofenergy output of a similar source with the same total volume and energyoutput where one half of the array is operated at one depth, and theother half of the array at a different depth, and the signal processedas explained above.

Methods according to the invention may provide improved quality seismicimages because of the substantial enhancement of the seismic signalacross the frequency band to do constructive summation of the up- anddown-going wave-fields from the source(s).

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

1. A method for acquisition and processing of marine seismic signals toextract up-going and down- going wave-fields from a seismic energysource, the method comprising: deploying at least two marine seismicenergy sources at different depths in a body of water and atsubstantially a same longitudinal position from a seismic vessel;actuating each of the seismic energy sources in a plurality of firingsequences, each sequence having a known, different time delay betweenfiring each source and a start of seismic signal recording; recordingseismic signals corresponding to each firing sequence; extractingseismic energy corresponding to each of the sources from the recordedseismic signals; and; extracting at least one of an up-going and adown-going wave-field using the extracted seismic energy therefrom. 2.The method of claim 1 wherein the time delays vary in at least one of arandom, semi-random and systematic manner between firing sequences. 3.The method of claim 1 wherein the extracting seismic energy from eachsource comprises time aligning the recorded signals with respect to afiring time of each source and coherency filtering the time alignedsignals with respect to the corresponding time aligned source firings.4. The method of claim 1 further comprising correcting for thedifferences in signatures of the sources towed at different depths. 5.The method of claim 1 further comprising designing sources towed atdifferent depths such that they have nearly identical signatures.
 6. Themethod of claim 1 wherein the signals are measured using at least one ofpressure sensors, pressure time gradient responsive sensors, pressuredepth gradient responsive sensors, particle motion responsive sensorsand combinations thereof.
 7. The method of claim 1 further comprisingpropagating the separated up-going and down-going wave-fields from eachsource to at least one of a water surface and a common reference depth,180 degree phase shifting one of the up-going and the down-goingwave-field, and summing the propagated, phase shifted up-going anddown-going wave-fields.
 8. The method of claim 7 where the extractedup-going and down-going wave-fields are propagated to at least one of awater surface and a common reference depth using angle dependent timeshifts based on known source depths and emission angles.
 9. The methodof claim 7 where the extracted up-going and down-going wave-fields arepropagated to at least one of a water surface and a common referencedepth using angle dependent linear phase shifts in the frequency domain.10. A method for marine seismic surveying, comprising: separatingup-going and down-going wave-fields from seismic energy emitted by atleast one marine seismic energy source; propagating the separatedup-going and down-going wave-fields from the at least one source to atleast one of a water surface and a common reference depth; 180 degreephase shifting one of the up-going and down-going wave-field; andsumming the propagated, phase shifted up-going and down-goingwave-fields.
 11. The method of claim 10 where the separated up-going anddown-going wave-fields are propagated to at least one of a water surfaceand a common reference depth using angle dependent time shifts based onknown source depths and emission angles.
 12. The method of claim 10where the separated up-going and down-going wave-fields are propagatedto at least one of a water surface and a common reference depth usingangle dependent linear phase shifts in the frequency domain.
 13. Themethod of claim 10 where one of the separated up-going and down-goingwave-field is 180 degree phase shifted before propagating thewave-fields to at least one of a water surface and a common referencedepth.
 14. The method of claim 10 where the up-going and down-goingwave-fields are propagated to at least one of a water surface and acommon reference depth before 180 degree phase shifting.
 15. The methodof claim 10 wherein the seismic energy is emitted by at least twosources operated at different depths and at substantially a samegeodetic position.
 16. A method for marine seismic surveying using atleast two seismic energy sources operated at different depths and atsubstantially a same source geodetic position, comprising: separatingenergy from each of the sources from the recorded signals; separatingup-going and down-going wave-fields corresponding to each source fromthe separated energy; propagating the separated up-going and down-goingwave-fields from each source to at least one of a water surface and acommon reference depth; 180 degree phase shifting one of the propagatedwave-fields; and summing the phase shifted, propagated wave-fields. 17.The method of claim 16 where the separated up-going and down-goingwave-fields are propagated to at least one of a water surface and acommon reference depth using angle dependent time shifts based on knownsource depths and emission angles.
 18. The method of claim 16 where theseparated up-going and down-going wave-fields are propagated to at leastone of a water surface and a common reference depth using angledependent linear phase shifts in the frequency domain.
 19. The method ofclaim 16 where one of the separated up-going and down-going wave-fieldis 180 degree phase shifted before propagating the wave-fields to atleast one of a water surface and a common reference depth.
 20. Themethod of claim 16 where the up-going and down-going wave-fields arepropagated to at least one of a water surface and a common referencedepth before 180 degree phase shifting.